A well known positioning system which is based on the evaluation of signals transmitted by beacons is GPS (Global Positioning System). The constellation in GPS consists of more than 20 satellites employed as beacons that orbit the earth. The distribution of these satellites ensure that usually between five and eight satellites are visible from any point on the earth.
Each of the satellites, which are also called space vehicles (SV), transmits two microwave carrier signals. One of these carrier signals L1 is employed for carrying a navigation message and code signals of a standard positioning service (SPS). The L1 carrier signal is modulated by each satellite with a different C/A (Coarse Acquisition) Code. Thus, different channels are obtained for the transmission by the different satellites. The C/A code, which is spreading the spectrum over a 1 MHz bandwidth, is repeated every 1023 chips, the epoch of the code being 1 ms. The carrier frequency of the L1 signal is further modulated with navigation information at a bit rate of 50 bit/s. The 50 Hz data bit stream of the navigation message is aligned with the C/A code transitions. The navigation information comprises in particular orbit parameters like ephemeris data. Ephemeris parameters describe short sections of the orbit of the respective satellite. Based on these ephemeris parameters, an algorithm can estimate the position and the velocity of the satellite for any time of about 2–4 hours during which the satellite is in the respective described section. Ephemeris data also comprise clock correction parameters which indicate the current deviation of the satellite clock versus a general GPS time. Further, a time-of-week TOW count is reported every six seconds as another part of the navigation message.
A GPS receiver of which the position is to be determined receives the signals transmitted by the currently available satellites, and a tracking unit of the receiver detects and tracks the channels used by different satellites based on the different comprised C/A codes.
In order to be able to detect the channels used by different satellites, the receiver has access to a replica of the C/A codes employed by each of the satellites. The receiver is thus able to compare the available C/A codes with the C/A codes in the received signals in a correlation procedure.
By evaluating measurements on the tracked signals, the receiver first determines the time of transmission of the ranging code transmitted by each satellite. Usually, the estimated time of transmission is composed of two components. A first component is the TOW count extracted from the decoded navigation message in the signals from the satellite, which has a precision of six seconds. A second component is based on counting the epochs and chips from the time at which the bits indicating the TOW are received in the tracking unit of the receiver. The epoch and chip count provides the receiver with the milliseconds and sub-milliseconds of the time of transmission of specific received bits. A detected epoch edge also indicates the code phase of a received signal.
Based on the time of transmission and the measured time of arrival TOA of the ranging code at the receiver, the time of flight TOF required by the ranging code to propagate from the satellite to the receiver is determined. By multiplying this TOF with the speed of light, it is converted to the distance between the receiver and the respective satellite. The computed distance between a specific satellite and a receiver is called pseudo-range, because the general GPS time is not accurately known in the receiver. Usually, the receiver calculates the accurate time of arrival of a ranging code based on some initial estimate, and the more accurate the initial time estimate is, the more efficient are position and accurate time calculations. A reference GPS time can, but does not have to be provided to the receiver by a communications network.
The computed distances and the estimated positions of the satellites then permit a calculation of the current position of the receiver, since the receiver is located at an intersection of the pseudo-ranges from a set of satellites. In order to be able to compute a position of a receiver in three dimensions and the time offset in the receiver clock, the signals from at least four different GPS satellites are required.
If navigation data are available on one of the receiver channels, the indication of the time of transmission comprised in a received signal can also be used in a time initialization for correcting a clock error in the receiver as the internal receiver clock is generally biased.
Currently, most GPS receivers are designed for outdoor operations with good signal levels from satellites.
In case of bad reception conditions, e.g. indoors, the tracking of signals is less reliable with such receivers. One of the problems is the cross-correlation effect between the satellites. When searching for a specific satellite signal, often an undesired cross-correlated signal from another satellite will be found. The signal-to-noise ratios of signals from different satellites vary within a wide range indoors, as the satellite signals undergo different attenuation. This implies that the signal from one satellite may be quite strong, while the signal from another satellite is rather weak. At the same time, the pseudonoise properties of the satellite signals provide only a limited selectivity during the correlation process. Signals from wrong satellites and code-phases are only attenuated by around 20 dB in the correlation procedure. Thus, if the differences in the signal-to-noise ratio of the different satellite signals are higher than this attenuation, then the signal from wrong satellites could interfere with a given channel. That is, a wrong satellite signal with a high signal level can be determined in the correlation procedure to be the desired satellite signal, in case the correct satellite signal has a low signal level. This makes normal tracking impossible.
In a known approach aimed at avoiding a wrong tracking, only those satellites are considered which have a limited difference in their signal-to-noise ratios. This approach has the disadvantage, however, that the receiver will often not be able to calculate the position when only signals from a few satellites are received, which is the most probable scenario indoors.
A known system called RAIM (Receiver Autonomous Integrity Monitoring), which is employed in airplanes, studies whether the measurements on tracked satellites are correct. However, RAIM is designed for use in good signal conditions and also requires reception of signals from at least 5 satellites.